Question

Perform the following subtraction. Provide both the hexadecimal _____________ and decimal _______________ answer. 12F16 - 8C16

The range of positive integers possible in an 8-bit two’s complement system is (Read this question carefully):

Question 8 options:

	1 to 256
	1 to 127
	-128 to 127
	1 to 128

1. Convert -132₁₀ to a 16-bit 2’s complement in binary ____________ and hexadecimal ______________.

Question 6 options:

Blank # 1
Blank # 2

Convert 110.75₁₀ to binary ______ and hexadecimal ______. Show the answer in both binary and hexadecimal.

Question 5 options:

Blank # 1
Blank # 2

Answer 1

1)
Perform the following subtraction. Provide both the hexadecimal A3 and decimal 163 answer. 12F16 - 8C16

2)
1 to 127

3)
Convert -132 to a 16-bit 2’s complement in binary 1111111101111100 and hexadecimal FF7C

4)
Convert 110.75 to binary 1101110.11 and hexadecimal 6E.C 
Show the answer in both binary and hexadecimal.

Explanation:
-------------
1)
12F
=> 1x16^2+2x16^1+Fx16^0
=> 1x256+2x16+Fx1
=> 1x256+2x16+15x1
=> 256+32+15
=> 303

8C
=> 8x16^1+Cx16^0
=> 8x16+Cx1
=> 8x16+12x1
=> 128+12
=> 140

12F - 8C = 303 - 140 = 163
let's convert 163 to hexadecimal

Divide 163 successively by 16 until the quotient is 0
163/16 = 10, remainder is 3
10/16 = 0, remainder is 10
Read remainders from the bottom to top as A3
Answer: A3

2)
-132
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 132 successively by 2 until the quotient is 0
   > 132/2 = 66, remainder is 0
   > 66/2 = 33, remainder is 0
   > 33/2 = 16, remainder is 1
   > 16/2 = 8, remainder is 0
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10000100
So, 132 of decimal is 10000100 in binary
So, 132 in normal binary is 0000000010000100
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   0000000010000100 is flipped to 1111111101111011
Step 3:. Add 1 to above result
1111111101111011 + 1 = 1111111101111100
so, -132 in 2's complement binary is 1111111101111100

Converting 1111111101111100 to hexadecimal
1111 => F
1111 => F
0111 => 7
1100 => C
So, in hexadecimal 1111111101111100 is 0xFF7C

4)
Converting 110.75 to binary
Convert decimal part first, then the fractional part
> First convert 110 to binary
Divide 110 successively by 2 until the quotient is 0
   > 110/2 = 55, remainder is 0
   > 55/2 = 27, remainder is 1
   > 27/2 = 13, remainder is 1
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101110
So, 110 of decimal is 1101110 in binary
> Now, Convert 0.75000000 to binary
   > Multiply 0.75000000 with 2. Since 1.50000000 is >= 1. then add 1 to result
   > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result
   > This is equal to 1, so, stop calculating
0.75 of decimal is .11 in binary
so, 110.75 in binary is 01101110.11

Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 01101110.1100 to hexadecimal
0110 => 6
1110 => E
1100 => C
So, in hexadecimal 01101110.1100 is 0x6E.C
Answer: 0x6E.C